# binomial interest rate tree

I may have missed the post on this, but are we expected to compute the rates int he tree or just use given rates to determine arbitrage free value? Also given YTM how do i bootstrap for spot rates? I can go from spot to forward, but cant get YTM to spot. example: assume trading at par M ytm 1 3.5 2 4.2 3 4.7 4 5.2 spots are… 3.5 4.2148 4.7352 5.2706

100 = 4.2/1.035 + 104.2/(1+x)^2 solve for X gives you 4.2148

Altho Schweser tries to show you how to calc the “Low” rate given the “high” or vice versa ( using an exponential expression ) , I don’t believe you’ll be asked to compute the rates. The rates should be given and you’re supposed to walk the tree , rendering the average values at the nodes backwards from maturity because face value is usually known at maturity

solve for Spot rates , one at a time , like CP shows . Next stage might be : 100 = 4.2/1.035 + 4.2/(1.042148^2)+104.2/(1+x)^3 solve for x. Then solve a 4-term expression , with the 3 terms as shown as above ad nauseam

actually next stage would be 4.7 coupon so would use 4.7, and 104.7